here is an alternative to the common approach at b. It can have a strategic meaning, for example to avoid being pressed into a low position (White a, Black b).
The normal answer is - see 4-5 point 3-3 approach for that. Other plays are less frequent: a, b and c are known from pro games.
For example, is more common in pro games than Black at a. The low stone
can cause Black to dislike being pressed down.
Black's idea is to play tenuki after here. White at a now makes thickness facing
.
For White ignoring the cover play by Black, see 3-5 point 3-3 approach cover, tenuki.
I think cutting will work for Black if the ladder doesn't work for White.
See double threat ladder-maker.